Second-order discontinuous Galerkin flood model: comparison with industry-standard finite volume models

Finite volume (FV) numerical solvers of the two-dimensional shallow water equations are core to industry-standard flood models. The second-order Discontinuous Galerkin (DG) alternative is well-known to perform better than first- and second-order FV to capture sharp flow fronts and converge faster at coarser resolutions, but DG2 models typically rely on local slope limiting to selectively damp numerical oscillations in the vicinity of shock waves. Yet flood inundation events are smooth and gradually-varying, and shock waves play only a minor role in flood inundation modelling. Therefore, this paper investigates two DG2 variants - with and without local slope limiting - to identify the simplest and most efficient DG2 configuration suitable for flood inundation modelling. The predictive capabilities of the DG2 variants are analysed for a synthetic test case involving advancing and receding waves representative of flood-like flow. The DG2 variants are then benchmarked against industry-standard FV models over six UK Environment Agency scenarios. Results indicate that the DG2 variant without local slope limiting closely reproduces solutions of the commercial models at twice as coarse a spatial resolution, and removing the slope limiter can halve model runtime. Results also indicate that DG2 can capture more accurate hydrographs incorporating small-scale transients over long-range simulations, even when hydrographs are measured far away from the flooding source. Accompanying details of software and data accessibility are provided.